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Author: Hermann Weyl

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13.02.2024
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PREFACE
One common thought holds together the following three lectures: Modern science, insofar as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed but pointing beyond itself. Or, as Franz Werfel expresses it in pregnant wording in one of his poems,
“Diese Welt ist nicht die Welt allein.”
Science finds itself compelled, at once by the epistemological, the physical and the constructive-mathematical aspect of its own methods and results, to recognize this situation. It remains to be added that science can do no more than show us this open horizon; we must not by including the transcendental sphere attempt to establish anew a closed (though more comprehensive) world.
I am grateful to Yale University for affording me an opportunity in these Terry Lectures of expressing this conviction by a description of the methodology of mathematics and physics. The lectures were originally written out in German. I do not want to omit acknowledging my indebtedness to my friend, Dr. Lulu Hofmann of Columbia University, New York, for the devoted assistance which she has ren- dered me in the translation of my manuscripts into English on this as well as on similar previous occasions. H. W.

Weyl's thesis: that modern science is compelled by its own methods and results to recognize the world as an open one, as a world not closed but pointing beyond itself, i.e. to a transcendental world of divinity. His arguments are worth the effort even though they unexpectedly presuppose a faith in the transcendental world. Here, the author offers three lectures which explore the metaphysical implications of science in light of his own philosophies.
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